Logarithm with no Calculator

I along with my friend find a way that is easy to calculate the logarithm base 10 to a few decimal accuracy with no calculator.
Expamle :

1) log 356746
2) log 9999689887964

For example 1, without a calculator, I can answer 5,5.

For example 2, without a calculator, I can say up to 4 decimals accuracy. The answer is 12,9999.

Do you want to know ?

First, look at digit number in front of the comma. To determine the first number in the answer, the number of digits in the number (in front of a comma) reduced by 1. Example : 356746 has 6 digits, then 6-1=5. The result is 5,xxx. Other examples :
9999689887964 has 13 digits, then 13-1=12, the result is 12,xxx

Second, look at the first number (856746)
If the number 8 or 9, then the first number in front of comma is 9
If the number is 1,

• If the next number is greater or equal 5 (> 5) (example: 165354), then the first number after comma is 2 (rounding the results)
• If the next number less than 5 (<5) (example: 134524), then the first number after comma is 1

Else, then add than number with 2, examlpe, 3 (in example 1), then 3+2 = 5.

So, the result is 5,5xxx

For example 2, I can count up to 4 decimal because the number has 9 in sequent at the beginning. This applies only to the number that have a number 9 in sequent at the beginning. Actually, level of accuracy depends on the digits of number 9. In the second example, 9999689887964 has 4 digits number 9 and the temporary result is 12,xxx. So the result is 12,9999.

For more accuracy level, experiments being conducted.